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the simultaneous operation of two vectors suppose the particle to be a bead on the wire AB,' Fig. 4. Move the win\ keeping it parallel to itself, until each of its particles is given a displacement represented by b. Simultaneously with the motion of the wire move the bead along the wire giving it a displacement equal to a. At the end of
these operations the bead arrives at the point 72. If both the wire and the bead are moved at constant rates the resultant vector c represents not only the resulting displacement but also the path of the particle.
10.   Rules for Adding Two Vectors.-—The results of the last three paragraphs furnish us with the following methods for adding two vectors graphically.
Triangle Method. Move one of the vectors, without changing its direction, until its origin falls upon the terminus of the other vector, then complete the triangle by drawing a vector the origin of which coincides with that of the first vector. The new vector is the resultant of the given vectors.
Parallelogram Method. ™ Move one of the vectors until its origin falls on that of the other vector, complete the parallelogram, and then draw a vector which has the common origin of the given vectors for its origin and which forms a diagonal of the parallelogram. The new vector is the resultant of the given vectors.
11.   Analytical Expression for the Resultant of Two Vectors.
a and b. Fie. 5, be two vectors and c their result-